Two baskets, A and B, contain apples. If 25 apples are taken from basket B and put in basket A, the numbers of apples in the baskets are interchanged. If instead 15 apples are taken from basket A and put in basket B, basket B then has twice as many apples as basket A. How many apples are in A and B respectively?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 70 and 95
Moving 25 from basket B to basket A swaps the counts only if basket B has 25 more than basket A. The second move then gives one equation.
Let basket A have \(a\); then basket B has \(a+25\)
After 15 are moved from basket A to basket B: basket A has \(a-15\), basket B has \(a+40\)
\(a+40=2(a-15)\), so \(a+40=2 a-30\)
\(a=70\), and basket B \(=70+25=95\)
Check: moving 15 gives 55 and 110, and 110 is twice 55
Basket A has 70 and basket B has 95 apples.
Why the other options are incorrect
Option (1) 80 and 105 — Incorrect. Moving 15 from basket A to basket B gives 65 and 120, and 120 is not twice 65.
Option (2) 75 and 100 — Incorrect. Moving 15 from basket A to basket B gives 60 and 115, and 115 is not twice 60.
Option (4) 95 and 70 — Incorrect. Moving 25 from basket B to basket A gives 120 and 45, not interchanged.